Apparatus, method and computer program product for weapon flyout modeling and target damage assessment

ABSTRACT

A weapon flyout simulation method, system, and computer program product, includes modeling a target as a plurality of ellipsoidal zones corresponding to a plurality of zones on the target, and performing hit/miss assessment on the target by determining if said trajectory of the weapon interferes with at least one of said plurality of ellipsoids.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a non-provisional application and claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Application No. 60/872,064, Atty. Docket No. 13346-239106, filed Dec. 1, 2006, entitled “Weapon Flyout & Damage Assessment Modeling” to Jaklitsch et al., of common assignee to the present application, the contents of which are incorporated herein by reference in their entirety.

BACKGROUND

1. Field

The present invention relates generally to weapon simulators and more particularly to modeling weapon flyout modeling and assessment of target damage.

2. Related Art

While modern simulation systems use extremely detailed visual models, these graphics entities are not well suited for mathematically determining whether a projectile of a weapon such as a missile having been fired at a target aircraft has physically hit the target aircraft. Most existing simulations model the simulated aircraft as a point in space, with the visual graphics rendered about the point, in an appropriate attitude. Impact is typically estimated probabilistically, based on proximity to the point target. Alternatively, any projectile that passes within a fixed radius may be declared as a “Hit” (i.e., target geometry is contained within a sphere).

One of the issues associated with performing an accurate assessment of a Hit or Miss engagement on an airborne target, with a missile or ballistic projectile, is the extremely high rate of motion involved in the scenario. In the engagement of a super-sonic aircraft with a hypersonic projectile or missile, the rate of closure between the two objects could easily reach Mach 5 (5500 ft/sec). At such rates, the time increment used for digital simulation is far too coarse to accurately assess if an impact has occurred. For example, if the simulation is running at a 30 Hz update rate (33.000 ms period), the objects may experience 183 ft of relative motion between two adjacent updates. Thus, the missile or the projectile of the missile could pass clear through the body of the aircraft from one sample rate to the next, without the interference test at each sample in time revealing that a collision had actually occurred.

What is needed is a Hit/Miss assessment model that overcomes the limitations of the conventional Hit or Miss engagement on an airborne target.

SUMMARY OF THE INVENTION

An exemplary system, method and computer program product for weapon flyout modeling, hit/miss assessment, and target damage assessment is disclosed herein, according to an exemplary embodiment.

In an exemplary embodiment of the invention, there may be provided a weapon flyout simulation method, which may include: modeling a target as a plurality of ellipsoidal zones corresponding to a plurality of zones on the target; and determining whether a trajectory of a weapon interferes with at least one of the plurality of ellipsoids.

In an exemplary embodiment, the weapon flyout simulation method may further include determining whether the weapon has reached a closest point of approach of the target. In an exemplary embodiment, the determining if a closest point of approach of the target has been reached may include: determining a relative position of the target with respect to the weapon; calculating an engagement closure state for the weapon based on the relative position; comparing the engagement closure state to a previous engagement closure state; and denoting that the closest point of approach has been reached based on a change in the engagement closure state.

In an exemplary embodiment, the step of determining if the trajectory of the weapon interferes with at least one of the plurality of ellipsoidal zones, according to the weapon flyout simulation method of the invention, may include: computing an elliptical magnitude at the point of closest approach based on parameters relating to the at least one ellipsoidal zone; and determining whether the trajectory of the weapon interferes with the at least one ellipsoidal zone based on the elliptical magnitude.

In an exemplary embodiment, the weapon flyout simulation method may further include transforming a trajectory of the weapon to a target zone coordinate frame for each of the plurality of ellipsoidal zones. In an exemplary embodiment, the step of determining whether a trajectory of a weapon interferes with at least one of the plurality of ellipsoids may be performed using the trajectory of the weapon in the target zone coordinate frame.

In an exemplary embodiment, the step of transforming a trajectory of the weapon to a target zone coordinate frame for each of the plurality of ellipsoidal zones may include: determining coordinates of the weapon and the target in an engagement coordinate frame; transforming a trajectory of the weapon from the engagement coordinate to a target body coordinate frame; and transforming the trajectory of the weapon from the target body coordinate to the target zone coordinate frame for each of the plurality of ellipsoids.

In an exemplary embodiment, the weapon flyout simulation method of the invention may further include computing impact coordinates on the target. In an exemplary embodiment, the step of computing impact coordinates on the target may include: calculating impact coordinates in a target zone coordinate system based on a point of closest approach for at least one of the plurality of ellipsoidal zones; and determining impact location in a target body coordinate system by rotating the impact coordinates from the target zone coordinate system.

In an exemplary embodiment, the weapon flyout simulation method of the invention may include computing a miss distance of the target by the weapon. In an exemplary embodiment, the step of computing a miss distance of the target by the weapon may include: computing a first vector representing the trajectory of the weapon; computing a second vector representing a distance a first trajectory point of the weapon and a centroid of at least one of the plurality of ellipsoidal zones; computing a third vector indicating a direction of a line running from the centroid of the at least one ellipsoidal zone perpendicular to the first vector based on the first and second vectors; scaling a magnitude of the third vector to unity to obtain a unit direction vector; and computing a miss vector based on a dot product of the unit direction vector and the second vector.

In an exemplary embodiment, the weapon flyout simulation method of the invention may include assessing impact damage on the target. In an exemplary embodiment, the assessing impact damage may be based on at least one of weapon lethality, target survivability, or zone sensitivity of at least one of the plurality of ellipsoidal zones. In an exemplary embodiment, the step of assessing impact damage may include: determining weapon lethality of the weapon; determining effective lethality of the weapon on the target based on the weapon lethality and a zone sensitivity of at least one of the plurality of ellipsoidal zones; and determining if the effective lethality exceeds a survivability threshold of the target.

In an exemplary embodiment, the weapon flyout simulation method of the invention may include assessing damage to the target based on proximate detonation of the weapon. In an exemplary embodiment, the step of assessing damage to the target based on proximate detonation of the weapon may include: computing a miss distance to a centroid of at least one of the plurality of ellipsoidal zones; computing a range loss for the miss distance; determining weapon lethality of the weapon; determining effective lethality of the weapon on the target based on the weapon lethality, a zone sensitivity of at least one of the plurality of ellipsoidal zones, and the range loss; and determining if the effective lethality exceeds a survivability threshold of the target.

In an exemplary embodiment of the invention, there may be provided a weapon flyout simulation system, including: a target modeling unit adapted to model a target as a plurality of ellipsoidal zones corresponding to a plurality of zones on the target; and a hit/miss assessment unit adapted to determine if a trajectory of a weapon interferes with at least one of the plurality of ellipsoids.

In an exemplary embodiment, the weapon flyout simulation system of the invention may include a closest point of approach calculation unit adapted to determine if the weapon has reached a closest point of approach of the target. In an exemplary embodiment, the hit/miss assessment unit may be adapted to compute an elliptical magnitude at the point of closest approach based on parameters relating to the at least one ellipsoidal zone, and determine whether the trajectory of the weapon interferes with the at least one ellipsoidal zone based on the elliptical magnitude.

In an exemplary embodiment, the weapon flyout simulation system of the invention may include a coordinate transformation unit adapted to transform a trajectory of the weapon to a target zone coordinate frame for each of the plurality of ellipsoidal zones. In an exemplary embodiment, the hit/miss assessment unit may determine whether a trajectory of the weapon in the target zone coordinate frame interferes with at least one of the plurality of ellipsoids.

In an exemplary embodiment, the weapon flyout simulation system of the invention may include an impact coordinate computation unit adapted to compute impact coordinates on the target based on a point of closest approach for at least one of the plurality of ellipsoidal zones. In an exemplary embodiment, the weapon flyout simulation system of the invention may also include a miss distance computation unit adapted to compute a distance by which the weapon has missed the target.

In an exemplary embodiment, the weapon flyout simulation system of the invention may include an impact damage assessment unit adapted to assess impact damage on the target based on at least one of weapon lethality, target survivability, or zone sensitivity of at least one of the plurality of ellipsoidal zones. In an exemplary embodiment, the weapon flyout simulation system of the invention may include a proximate damage assessment unit adapted to assess damage to the target based on proximate detonation of the weapon.

In an exemplary embodiment, the target comprises an aircraft. In an exemplary embodiment, the plurality of zones on the target include at least one of: a circumscribing sphere; a forward fuselage; an aft fuselage; a left sing; a right wing; a left rear stabilizer; a right rear stabilizer; a vertical stabilizer; and an extra surface.

According to an exemplary embodiment of the invention, there may be provided a computer readable medium embodying program logic, which, when executed, performs a method including: modeling a target as a plurality of ellipsoidal zones corresponding to a plurality of zones on the target; and determining whether a trajectory of a weapon interferes with at least one of the plurality of ellipsoids.

Further features and advantages of the invention, as well as the structure and operation of various embodiments of the invention, are described in detail below with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features and advantages of the invention will be apparent from the following, more particular description of a preferred embodiment of the invention, as illustrated in the accompanying drawings wherein like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements.

FIGS. 1A-1F illustrate an exemplary three-dimensional ellipsoidal interference model of an exemplary target aircraft, according to exemplary embodiment of the invention.

FIG. 2 depicts an exemplary block diagram of an exemplary weapon flyout dynamics model, according to an exemplary embodiment of the invention.

FIGS. 3A-3C illustrate an exemplary process flow diagram for weapon kinematics flyout simulation, according to an exemplary embodiment of the invention.

FIG. 4 illustrates an exemplary process flow diagram for weapon guidance processing for an IR Seeker missile, according to an exemplary embodiment of the invention.

FIG. 5 illustrates an exemplary Generalized Guidance Filter 500 implementing the Difference Equation, according to an exemplary embodiment of the invention.

FIG. 6 illustrates an exemplary process flow diagram for weapon guidance processing of a Laser Beam-Riding Seeker (RBS-70), according to an exemplary embodiment of the invention.

FIG. 7 illustrates an exemplary Hit/Miss Assessment process flow diagram for a target aircraft, according to an exemplary embodiment of the invention.

FIG. 8 illustrates an exemplary process flow diagram for determining whether a zone of the aircraft intercepts the weapon trajectory, according to an exemplary embodiment of the invention.

FIG. 9 illustrates an exemplary process flow diagram for calculating the aircraft damage assessment, according to an exemplary embodiment of the invention.

FIG. 10 depicts an exemplary computer system that may be used in implementing an exemplary embodiment of the present invention.

DETAILED DESCRIPTION OF AN EXEMPLARY EMBODIMENT OF THE PRESENT INVENTION

An exemplary embodiment of the invention is discussed in detail below. While specific exemplary embodiments are discussed, it should be understood that this is done for illustration purposes only. A person skilled in the relevant art will recognize that other components and configurations can be used without parting from the spirit and scope of the invention.

The exemplary embodiments of the invention are described using a missile as an exemplary weapon. It should be understood, however, that the present invention is not limited to one type of weapon and may be used for any types of weapons, including, e.g., but not limited to, cruise missiles, anti-aircraft weapons, anti-ship weapons, anti-tank weapons, anti-submarine weapons, anti-personnel weapons, guided missiles, remote-control guided missiles, homing-guided missiles, and/or unguided ballistic munitions, etc. Any reference made herein to a missile should be construed to include any type of weapon. Further, the exemplary embodiments of the invention may be described with reference to an aircraft as exemplary targets. It should also be understood that a present invention may be used for hit/miss and damage assessment on any type of target including, e.g., but not limited to, aircrafts, aircraft carriers, ships, tanks, and/or any other type of mobile and/or stationary targets. Accordingly, exemplary references made in the FIGs. and the corresponding description should not be seen as limiting the present invention to a certain type of weapon or a certain type of target.

Exemplary embodiments of the present invention provide a system, method, and/or computer program product that provide modeling of a target aircraft interference geometry using open-source performance data, simulation of weapon fly-out dynamics, assessment of miss/hit of the target aircraft, assessment of impact damage of the target aircraft, and/or assessment of proximity detonation damage on the target aircraft.

According to an exemplary embodiment of the invention, in order to maximize fidelity and provide user flexibility, the weapon and/or the target may be modeled at a high level of parametric abstraction to cover a wide range of weapons such as, for example, but not limited to, missiles, unguided ballistic missiles, remote-control guided missiles, etc., as well as a wide range of targets such as, e.g., but not limited to, helicopters, bombers, tankers, transport aircrafts, and/or cargo aircrafts, etc. In an exemplary embodiment, the model having a high level of parametric abstraction may be adapted to each specific case of a weapon and target. In an exemplary embodiment, user-accessible model data tables may be adapted to define the parameters for various weapons and targets.

Exemplary Target Interference Geometry Modeling

The modeling approach according to embodiments of the present invention may enable a high fidelity simulation of the engagement dynamics, using a physics-based implementation. For example, it may be possible to determine the part of a target aircraft has been hit, and provide impact coordinates for the part that has been hit. Further, the modeling approach according to exemplary embodiments of the invention may significantly reduce risk of not detecting a true “Hit” by de-coupling the model development from the parametric data. Thus, development of a software application embodying various aspects of the present invention may proceed independently of specific data pertaining to the weapons and/or targets.

Further, according to an exemplary embodiment of the invention, modeling data to be populated at iterative levels of detail. Thus, in cases where obtaining very detailed parametric data may be difficult or impractical, less specific data estimates may be allowed for modeling the weapon and/or the target. For example, in some instances the exact parameters of the weapon or target may be unavailable due to classification, or may not even be included in the manufacturer's specifications. Also, there may be US export issues with specific weapons data. In such cases, the models may be populated with generic data, where such data is available, or estimated, where such data is not available, and later revised with additional levels of specific detail. In addition, the parametric approach according to exemplary embodiments of the present invention may provide more flexibility by allowing a user to easily tune the performance parameters or even define new models.

In an exemplary embodiment, it may be assumed that the weapon as well as the target aircraft are in a normal, fixed coordinate frame (X North, Y East, Z Down), hereinafter referred to as the Engagement Coordinate Frame (ECF). In an exemplary embodiment, any coordinates in the ECF may be expressed in the Gunner Centric Coordinate System (GCCS) (X East, Y North, Z up) by applying a simple transform:

XForm_(ECF) _(—) _(to) _(—) _(GCCS)=DCM[Yaw=90°,Pitch=0,Roll=180°]  (Eq. 1)

In an exemplary embodiment, in order to create a high fidelity physical simulation and hit/miss assessment of the weapon to the target aircraft, a physical geometry of aircraft entities may be modeled such that it may be possible to accurately determine if a projectile of the weapon has hit the aircraft. As previously discussed, most convent ional simulation systems use extremely detailed graphics models that may not be suited for mathematically determining whether a projectile has physically hit a target aircraft. Thus, many existing simulations may fly the simulated aircraft as, for example, a point in space, with the visual graphics rendered about the point, in an appropriate attitude. In such conventional systems, impact may be estimated probabilistically based on proximity to the point target or may be estimated deterministically based on passes of a projectile of the weapon within a fixed radius of the point.

Accordingly, in an exemplary embodiment of the invention, in order to provide a higher fidelity approximation of target physical geometry, the target aircraft may be modeled using a series of three-dimensional ellipsoidal zones corresponding to approximate key features of the target aircraft. For example, the target aircraft may be divided into ten different zones, such as, but not limited to, the circumscribing sphere, the forward fuselage, the aft fuselage, the left wing, the right wing, the left rear stabilizer, the right rear stabilizer, the vertical stabilizer, and two extra surfaces. Thereafter, each zone may be modeled as an ellipsoid. In an exemplary embodiment, these ellipsoidal zones may be used to determine if a trajectory of the weapon has passed through the target aircraft.

Referring now to FIGS. 1A-1F, there is illustrated an exemplary three-dimensional ellipsoidal interference model of an exemplary target aircraft, according to an exemplary embodiment of the invention. In FIGS. 1A-1F, the exemplary aircraft is an F-16 jet and the exemplary interference model may include a series of 7 ellipsoidal structures. FIG. 1A-1F illustrate the left-rear elevated view 102, left-front elevated view 104, front view, rear view 108, right view 110, and left view 112, respectively. In an exemplary embodiment, the ellipsoids may have different stretching, lateral offset, and angular rotation, so as to closely approximate various parts of the aircraft geometry. In an exemplary embodiment, each ellipsoid may model a specific zone on the aircraft and may be used to assess impact damage to the specific zone which it models. This basic technique may be easily adapted to model a wide range of targets, such as, e.g., but not limited to, various aircraft types.

The use of ellipsoids may provide a very easy and convenient technique for building reasonably accurate physical interference models, with a minimum of effort, as well as evaluating the model for physical interference (e.g., ballistic impact) with minimal computational load. In an exemplary embodiment, where the target is embodied as an aircraft, a standard model structure for the target aircraft may include, e.g., but not limited to, 10 zones, which may be arranged, in an exemplary embodiment, as shown in Table 1 below.

TABLE 1 Target Aircraft ellipsoidal Zones Zone 0 Circumscribing Sphere Zone 1 Forward Fuselage Zone 2 Aft Fuselage Zone 3 Left Wing Zone 4 Right Wing Zone 5 Left Rear Stabilizer Zone 6 Right Rear Stabilizer Zone 7 Vertical Stabilizer Zone 8 First Extra Surface Zone 9 Second Extra Surface

In an exemplary embodiment, each zone (ellipsoid) may be defined by a set of parameters, such as, e.g., but not limited to, nice (9) parameters. In an exemplary embodiment, the nine parameters defining a zone may include:

-   -   {a, b, c, x0, y0, z0, zone_yaw, zone_pitch, zone_roll}

In an exemplary embodiment, these parameters may define the ellipsoidal surface of each zone in accordance to the following equation:

$\begin{matrix} {{\frac{\left( {x - x_{0}} \right)^{2}}{a^{2}} + \frac{\left( {y - y_{0}} \right)^{2}}{b^{2}} + \frac{\left( {z - z_{0}} \right)^{2}}{c^{2}}} = 1} & \left( {{Eq}.\mspace{14mu} 2} \right) \end{matrix}$

In this equation, the offset parameters (x₀, y₀, z₀) denote the center of the ellipsoid in {x, y, z} vector space. The dimensions of the resulting surface in {x, y, z} vector space are directly related to the gain parameters (a, b, c). Thus, by changing the coefficient (a, b, c), the surface may be made spherical (i.e., where a=b=c), the surface may be stretched to approximate the cylindrical shape of a fuselage (e.g., where b=c<a), or flattened to approximate the surface of a wing or stabilizer (e.g., where a is very small compared to b and c). The location of the shaped surface in vector space may be controlled by the offset parameters (x0, y0, z0). By changing the offset parameters, a modeled surface may be moved forward/backward, left/right, or up/down within the aircraft body coordinate system. Further, in an exemplary embodiment, a rotational transformation (yaw, pitch, roll) may be used to rotate the surface to an angle necessary to approximate a specific aircraft feature or region. In an exemplary embodiment, the rotational transform may define a local coordinate frame for the ellipsoid with respect to aircraft body coordinates.

In an exemplary embodiment of the invention, as depicted in FIGS. 1A-1F, seven (7) different ellipsoids are combined, each ellipsoid appropriately scaled, offset, and rotated, to model an F-16 aircraft. In other types of aircraft, a greater or lesser number of ellipsoids may be adapted to represent the various parts of the aircraft. For example, a generic fighter aircraft with a jet engine may be modeled using six (6) ellipsoids (e.g., two wings, two rear stabilizers, vertical stabilizer, and the main fuselage).

In an exemplary embodiment, various types of aircrafts may be grouped into eight (8) broad categories, each category having a specific number of ellipsoids to model the aircraft. In an exemplary embodiment, the aircrafts may be categorized as, e.g., but not limited to, fast jets, tankers, commercial airliners, large propeller jet, small propeller jet, helicopters, and Unmanned Aerial Vehicles (UAV). In an exemplary embodiment, a generic aircraft model may be designed for each aircraft category and may later be parameterized for the specific aircraft being simulated. Accordingly, it is possible to model a wide variety of aircrafts with a reasonable fidelity coverage.

Exemplary Weapon Flyout Dynamics Modeling

According to an exemplary embodiment of the invention, the weapon flyout dynamics model may replicate the physics associated with flying a weapon through space. The model may be defined at a level of abstraction that enables it to represent a wide range of various weapons, yet faithfully replicate the physics involved with the weapon projectile flyout. In an exemplary embodiment, the same weapon flyout model may be used for both guided and un-guided weapons. In an exemplary embodiment, a general model may be constructed for the guided weapons and the un-guided weapons may use the same model wherein the guidance parameters are inapplicable.

FIG. 2 depicts an exemplary block diagram of an exemplary weapon flyout dynamics model 200, according to an exemplary embodiment of the invention. As illustrated, the model 200 may include subsystems including a Weapon Kinematics Processing 202, Guidance Processing 204, and a Weapon Properties Data File 206. In an exemplary embodiment, the Weapon Kinematics Processing 202 may execute generalized kinematics equations common applicable to all weapons and projectiles. The Guidance Processing 204 may include an executable module generating real-time steering vector commands to the Weapon Kinematics Processing 202. In an exemplary embodiment, the Guidance Processing 204 may be type-specific, including type definitions for specific weapons such as, e.g., but not limited to, IR Homing, Laser Beam Rider, Un-guided, etc.

The Weapon Properties Data File 206 may include a data file, which may be a text file, providing the parametric input to configure the generalized kinematics equations to reflect the performance parameters of a specific weapon. The Weapon Properties Data File 206 may also provide parametric input to configure the guidance processing algorithms of the Guidance Processing 204. In an exemplary embodiment, such parametric input may include, e.g., but not limited to, type definitions for specific weapons as well as data pertaining to properties of specific weapons, which may needed for modeling the guidance performance of the specific weapons.

According to an exemplary embodiment of the invention, the Weapon Kinematics Processing 202 may include a target modeling unit 210, a coordinate transformation unit 212, a hit/miss assessment unit 214, a point of closest approach (PCA) determination unit 216, an impact coordinate computation unit 218, a miss distance computation unit 220, an impact damage assessment unit 222, and a proximate damage assessment unit 224.

In an exemplary embodiment, the target modeling unit 210 may model the target in ellipsoidal zones, as previously described. For example, the target modeling unit 210 may receive parametric data regarding the target aircraft and model the aircraft into exemplary, but non-limiting, 10 ellipsoidal zones, each zone corresponding to a section of the aircraft.

In an exemplary embodiment, the coordinate transformation unit 212 may perform zone transformations from one coordinate system to another. For example, the coordinate transformation unit 212 may transform coordinates of a point in a three-dimensional space from any of the Engagement Coordinate Frame (ECF), Aircraft Body Coordinate Frame, and Aircraft Zone Coordinate Frame, to one another. The coordinate transformation unit 212 may also perform transformation from any of these coordinate frames to weapon's Attitude Eulerian angles. These transformations will be described in more detail later.

In an exemplary embodiment, the hit/miss assessment unit 214 may perform assessment on whether a trajectory of the weapon passes through at least one zone of the target aircraft. If so, the hit/miss assessment unit 214 may declare the weapon as a “Hit”.

In an exemplary embodiment, the hit/miss assessment unit 214 may make this determination by utilizing a point of closest approach of the weapon. The point of closest approach may denote the point detected by the simulation at which the weapon was closest to the target aircraft. In an exemplary embodiment, the PCA determination unit 216 may be responsible for calculating the point of closest approach. Calculation of the point of closest approach will be discussed in detail later.

In an exemplary embodiment, the impact coordinate computation unit 218 may compute the coordinates at which the weapon may hit the target. Alternatively, if it is determined that the weapon has missed the target, the miss distance computation unit 220 may calculate the distance by which the weapon missed the target. Computation of the impact coordinates and miss distance are discussed later in detail.

In an exemplary embodiment, the impact damage assessment unit 222 may measure the damage on the target aircraft by the weapon impact. If the weapon does not hit the aircraft directly, but detonates near the aircraft, the aircraft may be damaged by the proximate detonation of the weapon. In an exemplary embodiment, the proximate damage assessment unit 224 may measure such proximate damage on the target aircraft. Computation of impact damage and proximate damage are discussed later in detail.

According to various exemplary embodiments of the weapon flyout dynamics modeling approach, the user may be allowed to tune the parametric performance of simulated weapons and define new models for emerging weapons with a minimum of effort. For example, if the guidance functions of a new missile are more esoteric than the algorithms contained in existing type definitions, the user may create a new type guidance model for the missile. However, most existing air-defense missiles can be classified as one of infrared (IR) Guided missiles, Laser Beam Rider missiles, and Un-guided missiles. Thus, for most existing air-defense missiles, the user may use one of the guidance data of one of these weapon types.

According to an exemplary embodiment of the invention, the parametric inputs to the weapon flyout dynamics model may include, e.g., but not limited to, weapon properties, initial conditions, and perturbations. Weapon properties are related to the properties of the weapon such as, e.g., but not limited to, the missile, which do not change from one simulation scenario to the next. In an exemplary embodiment, the weapon properties may be stored a Weapon Properties Data File 206 as, e.g., but not limited to, text files including such data. In an exemplary embodiment, the initial conditions may include scenario-dependent conditions that are set at the moment the weapon is launched. In an exemplary embodiment, perturbations may include parameters that are real-time inputs to the simulation, including, e.g., but not limited to, wind, steering commands, etc.

Exemplary Weapon Kinematics Processing Inputs

In an exemplary embodiment, weapon properties parametric input to the Weapon Kinematics Processing 202 may include, e.g., but not limited to, “acceleration vs. time characteristic”, weapon's “projected area vector”, “wind sensitivity coefficient”, “missile maneuverability limit”, “maximum range of interest”, and data relating to warhead lethality and propagation. Table 2 below depicts exemplary weapon properties for Weapon Kinematics Processing 202, according to an exemplary embodiment of the invention.

TABLE 2 Weapon Properties for Kinematics Processing PARAMETER DESCRIPTION UNITS Acceleration vs. Data table of acceleration vs. time, in Meters/ Time increments of τ, where τ denotes the Sec² update interval Area_Vec {Area_(x), Area_(y), Area_(z)} vector giving Meters² the weapon's projected area onto each of the three axes in the weapon body coordinate system. K_(w) Wind sensitivity coefficient, 1/Meter³ describing the acceleration resulting from wind. G_limit Missile maneuverability limit (i.e., G max turning acceleration) Maximum Range Flight range beyond which the Meters of Interest simulated flyout may be stopped for non-detonated missiles Warhead_μ Mean value of warhead lethality Damage Units Warhead_σ Standard Deviation of warhead Damage lethality Units Warhead_n Warhead propagation exponent (1/ Dimension- R^(n)) less

In an exemplary embodiment, the “acceleration v. time characteristic” may include a data table of acceleration vs. time, in increments of τ, where τ denotes the update interval. In an exemplary embodiment, the time interval may be, e.g., but not limited to, 30 ms. The “acceleration v. time characteristic” may be a scalar quantity and may include both thrust & drag effects along the weapon x-axis (i.e., the longitudinal body axis). The “acceleration v. time characteristic” may not include other environmental accelerations (e.g., but not limited to, G, G rate of Turn, Windage, etc.), which may be computed in the Earth-fixed Engagement Coordinate Frame.

In an exemplary embodiment, the “acceleration v. time characteristic” may include a level of parametric abstraction designed to increase simulation fidelity without compromising the ability to closely replicate device physics. This characteristic may include the acceleration along the weapon (e.g., the missile) axis or the projectile longitudinal axis, including, e.g., but not limited to, thrust, drag, and variable-mass effects. In an exemplary embodiment, to the extent that detailed information is available for thrust, drag, and mass, the acceleration may be accurately pre-calculated from the known data. Alternately, if detailed open-source data is not available, the acceleration characteristic mat be computed based on the approximate flight time vs. range. In either case, the basic model may remain unaffected while the parametric data is modified.

In a further exemplary embodiment of the invention, the level of abstraction used for “acceleration v. time characteristic” may also enable differences in booster design to be captured without changing the basic model. For example, a two stage booster may include two independent periods of acceleration, each followed by drag-induced deceleration, and finally a second stage burn-out. A single stage boost, however, may only include one period of acceleration followed by drag-induced deceleration, and a ballistic shot may only include drag-induced deceleration. The acceleration v. time characteristic may define the various booster stages.

In an exemplary embodiment, the weapon's “projected area vector” may included a three dimensional vector {Area_(x), Area_(y), Area_(z)} providing the weapon's projected area onto each of the three axes in the weapon body coordinate system. The projected area vector may be used along with the wind sensitivity coefficient to compute the acceleration induced by wind-load on the missile or projectile. In an exemplary embodiment, the wind sensitivity coefficient (K_(w)) may describe the acceleration result from the wind such that a=K_(w)·V_(w) ²·A, where a is the acceleration, A is area, and V_(w) is the wind velocity (equivalent to the combination of aero terms 0.5ρCd/m). In an exemplary embodiment, the wind acts on the projected area, A, and produces an acceleration of K_(w)·V_(w) ²·A.

In an exemplary embodiment, the “missile maneuverability limit” (G) may specify the maximum turning acceleration for the weapon. In an exemplary embodiment, the missile maneuverability limit may be a result of aerodynamic limitations, but can be expressed parametrically. In an exemplary embodiment, the maximum range of interest may specify a max range, beyond which the weapon flyout is discontinued for non-detonated weapons.

In an exemplary embodiment, the “warhead lethality” may include, e.g., but not limited to, the mean value of warhead lethality (Warhead_μ), the standard deviation of warhead lethality (Warhead_σ), and warhead propagation exponent (Warhead_n).

In an exemplary embodiment of the invention, initial conditions parametric inputs for the Weapon Kinematics Processing 202 may include, e.g., but not limited to, “initial weapon position”, “initial weapon attitude”, and “launch/missile speed”. In an exemplary embodiment, the “initial weapon position” may include an {x, y, z} initial position vector in the Engagement Coordinate Frame (ECF), measures in, e.g., but not limited to, Meters. The “initial weapon attitude” may include a {yaw, pitch, roll} initial attitude measured in, e.g., but not limited to, Radians. The “launch/missile speed” may indicate the initial weapon scalar speed in, e.g., but not limited to, Meters/Sec. Table 3 below shows exemplary initial conditions parametric inputs for the Weapon Kinematics Processing 202, according to an exemplary embodiment of the invention.

TABLE 3 Initial Conditions for Kinematics Processing PARAMETER DESCRIPTION UNITS Initial Missile Position {x, y, z} Initial Position Vector Meters (Missile_Pos_ECF₀) in the ECF Initial Missile Attitude {Yaw, Pitch, Roll} Initial attitude Radians Launch/Missile Speed Missile Initial Speed Meters/Sec

In an exemplary embodiment of the invention, the real-time perturbations parametric inputs for the Weapon Kinematics Processing 202 may include, e.g., but not limited to, “wind velocity” and “steering vector”. The “wind velocity” may include an {x, y, z} wind velocity vector in the Engagement Coordinate Frame (ECF). The “steering vector” may include a {Az, El} attitude correction vector in the weapon body coordinates. Table 4 below shows exemplary real-time perturbations parametric inputs for the Weapon Kinematics Processing 202, according to an exemplary embodiment of the invention.

TABLE 4 Real-Time Perturbations for Kinematics Processing PARAMETER DESCRIPTION UNITS Wind Velocity {x, y, z} Wind Velocity Vector Meters/Sec (Wind_Vel_ECF) in the ECF Steering Vector Required {Az, El} Attitude Correction Radians Vector in missile body coordinates (Req_Steer_BC)

Exemplary Guidance Processing Inputs

In an exemplary embodiment, the parametric input, e.g., weapon properties, initial conditions, and real-time perturbations, for the Guidance Processing 204 may vary depending on the type of weapon being simulated. For example, the parametric inputs to a Guidance Processing 204 of a Infrared (IR) seeker may be different from the parameter used for a laser beam-rider missile or an unguided missile. For purposes of illustration, the exemplary Guidance Processing 204 parametric inputs for an IR Seeker are herein described.

In an exemplary embodiment, the weapon properties parametric inputs for Guidance Processing 204 of an IR Seeker may include, e.g., but not limited to, a guidance filter proportional gain (K_(P)), a guidance filter integral gain (K_(i)), a guidance filter differential gain (K_(d)), a gimbal limit, and an aim-point dynamics bias.

In an exemplary embodiment, the K_(P), K_(i), and K_(d) parameters may specify the proportional, integral and differential gains of a guidance filter, respectively, if this level of detail is known. In an exemplary embodiment, these parameters may be measured using transfer functions from measured error to steering vector. If all that is known is max rate of turning acceleration for the missile, Kp, Ki, and Kd may be set to 1, 0, 0, respectively, and the maximum rate of turn may be specified through the gimbal limit parameter in the Weapon Kinematics Processing 202.

In an exemplary embodiment, the gimbal limit may specify the maximum rate and/or the free range of the seeker gimbal. In an exemplary embodiment, an angular error beyond this range may cause the weapon to move beyond the range of detection and the target track to be lost.

In an exemplary embodiment, the aim-point dynamics bias may be a mechanism for programming profile effects such as, e.g., but not limited to, pop-up or corkscrew flyout. In an exemplary embodiment, the dynamic aim-point bias may be used to cause the missile to lead the target, or otherwise bias the aim-point away from the target centroid. Table 5 below shows exemplary weapon properties parametric inputs for the Guidance Kinematics Processing 204 of an IR Seeker missile, according to an exemplary embodiment of the invention.

TABLE 5 Weapon Properties for Guidance Processing of an IR Seeker PARAMETER DESCRIPTION UNITS KP Guidance Filter Proportional Gain Dimensionless Ki Guidance Filter Integral Gain Sec Kd Guidance Filter Differential Gain 1/Sec Gimbal_limit {Az, El} ordered pair, denoting the Radians max ± free range of the seeker. Aim-point Data table of {Az, El} ordered pairs vs. Radians Dynamic Bias time, in increments of τ, where τ denotes the update interval (30 ms)

In an exemplary embodiment, initial conditions parametric inputs for the Guidance Processing 204 of an IR Seeker may include, e.g., but not limited to, target lock/unlock, warhead enable, target position state, target altitude state, and warhead detonate command. In an exemplary embodiment, the aim-point static bias may denote the aim-point bias to be added as an offset to the aim-point error and may be specified by the weapon operator immediately prior to launch. The aim-point static bias may be specified as a signed {Az, El} angular bias having an aim-point with respect to the target and may be added to the steering vector. Table 6 below shows exemplary initial conditions parametric inputs for the Guidance Kinematics Processing 204 of an IR Seeker missile, according to an exemplary embodiment of the invention.

TABLE 6 Initial Conditions for Guidance Processing of an IR Seeker PARAMETER DESCRIPTION UNITS Aim-point {Az, El} ordered pair, denoting aim-point bias Radians Static Bias to be applied as an offset to the aim error

In an exemplary embodiment, the real-time perturbations parametric inputs for the Guidance Processing 204 may include, e.g., but not limited to, aim-point static bias. In an exemplary embodiment, the “target lock/unlock” parameter may denote successful target lock. The target may be unlocked during flyout to simulate a loss of track event or seek seeker malfunction. In an exemplary embodiment, the “warhead enable” parameter may denote proper functioning of the warhead fusing. The “target position state” and “target attitude state” may respectively denote the target position vector and the target Eulerian angles. The “warhead detonate command” may denote the command used to detonate the warhead at times other than normal fused detonation on the impact of the point of closest approach of the weapon. Table 7 below shows exemplary real-time perturbations parametric inputs for the Guidance Kinematics Processing 204 of an IR Seeker missile, according to an exemplary embodiment of the invention.

TABLE 7 Real-Time Perturbations for Guidance Processing of an IR Seeker PARAMETER DESCRIPTION UNITS Target Lock/ Boolean State Input denoting successful Boolean Un-Lock target lock if True. T/F Warhead Boolean State Input denoting proper Boolean Enable functioning of the warhead fusing. False T/F denotes detonate malfunction Target Position {x, y, z} Target Position Vector Meters State Target Attitude {Yaw, Pitch, Roll} Target Eulerian Angles Radians State Warhead Boolean Command to detonate warhead at Boolean Detonate Cmd times other than normal fused detonation T/F

In an exemplary embodiment of the invention, the seeker failures may be simulated by setting the “target lock/unlock” to “False”, causing the seeker to stop tracking and instead output a static steering vector {0,0} to the Kinematics Processing 202. Also, successful ECM events, such as, e.g., but not limited to, acquisition of a flare by an IR Seeker, can be simulated by transferring the missile aim-point off the target and onto a bogus object, such as, e.g., but not limited to, a flare, and then continuing to run the simulation with the missile seeking the bogus object.

The Guidance Processing 204 of other types of weapons such as, e.g., but not limited to, may be simulated with parameters that are similar to the parameters for an IR Seeker discussed above. For example, for a laser beam rider missile, all the Guidance Processing parameters, including the missile properties, initial conditions, and real-time perturbations, are similar to the parameters used for the Guidance Processing 204 of an IR Seeker, except that a laser aiming state in the form of {Yaw, Pitch} Laser Eulerian angle is used instead of the “target position state” and “target attitude state” parameters.

In an exemplary embodiment, un-guided missiles may be treated as a subset of the guided missile case. However, because there is no seeker, the “steering vector” input to the Weapon Kinematics Processing 202 may be held statically at {0,0}. Accordingly, a model similar to the one discussed for an IR Seeker may be used. In an alternative exemplary embodiment, however, computational efficiency may be increased by using a sub-set of the more general case for the Weapon Kinematics Processing 202, so that time is not wasted computing parameters that are known to be not applicable.

Exemplary Missile Kinematics Processing

FIGS. 3A-3C collectively illustrate an exemplary process flow diagram for weapon (e.g., missile) kinematics flyout simulation, according to an exemplary embodiment of the invention.

The exemplary physical constants for this process 300 may be as follows:

Gravity: G_Acc_Scalar = 9.80665 (m/sec²) Update Period: T = .033000 (sec)

Beginning with FIG. 3A, process 300 for initializing weapon settings may start at 302 and may continue to initialize Missile Position, block 304:

Mis_Pos_ECF0={X,Y,Z}  (Eq. 3)

According to an exemplary embodiment, Missile Attitude (i.e., aim orientation) may then be initialized with respect to the ECF, block 306:

Mis_Att_ECF0={Yaw,Pitch,Roll}  (Eq. 4)

Initial Missile Velocity in an exemplary embodiment, may then, in an exemplary embodiment, be initialized in Body Centered Coordinates, block 308:

Mis_Vel_BC0={Initial speed,0,0}  (Eq. 5)

In an exemplary embodiment, Missile Attitude Direction Cosine Matrix (DCM) may then be computed from Missile Attitude Eulerian angles (Mis_Att_ECF), block 310. Computation of DCM from Eulerian angles are discussed later in detail.

EECF_to_Missile,0=DCM_XForm[{Yaw,Pitch,Roll]  (Eq. 6)

Missile Velocity may then be transformed to Missile Velocity Vector in ECF, block 312:

Mis_Vel_ECF0=Transpose[EECF_to_Missile,0]·Mis_Vel_BC0  (Eq. 7)

Gravity Acceleration Vector may then be formed in the ECF, block 314, according to any exemplary embodiment. In an exemplary embodiment, the acceleration of gravity may be aligned with the positive z axis in the ECF:

Gravity_Acc_ECF={0,0,G_Acc_Scalar}  (Eq. 8)

Thereafter, process 300 may continue to A, where the missile may be launched and the flyout loop may begin, block 316.

FIG. 3B illustrates an exemplary process 320 of weapon flyout loop, according to an exemplary embodiment of the invention. Starting at block 316, corresponding to A in process 300, the process 320 may continue to compute current missile acceleration, in block 322. In an exemplary embodiment, Accel_(n)=Scalar from Acceleration vs. time table.

In an exemplary embodiment, a Missile Linear Acceleration Vector may be formed in the missile body coordinates, in block 324:

Mis_Lin_Acc_BCn={Acceln,0,0}  (Eq. 9)

Thereafter, in an exemplary embodiment, a wind-induced acceleration may be computed in ECF (Wind_Acc_ECF). Computation of wind-included acceleration is discussed later in detail.

In an exemplary embodiment, an applicable Guidance Function relating to the missile may be executed, in block 328. The Guidance Function may return the Required Steering Vector (Req_Steer_BC) of the missile. The Required Steering Vector may not have the effects of acceleration limiting. In an exemplary embodiment, the Required Steering Vector may be a {Yaw, Pitch} Eulerian.

In an exemplary embodiment, the Actual Steering Vector (Act_Steer_BC) may be computed by applying acceleration limiting to the Required Steering Vector, in block 330. Application of acceleration limits to missile steering are discussed later in detail.

In an exemplary embodiment, the Missile Steering Accelerations may be computed Missile Body Coordinates (Mis_Steer_Acc_BC) based on the Actual Steering Vector, in block 332. Computation of missile body accelerations due to steering is discussed later in detail.

In an exemplary embodiment, the Missile Body Acceleration may be computed by summing the Linear Body Acceleration and the Steering Accelerations, in block 334:

Mis_Body_Acc_BCn=Mis_Lin_Acc_BCn+Mis_Steer_Acc_BCn  (Eq. 10)

The Missile Body Acceleration, in an exemplary embodiment, may then be transformed to ECF as (Mis_Acc_ECF), in block 336:

Mis_Acc_ECF_(n)=Transpose[E_(ECF) _(—) _(to) _(—) _(Missile,n)]·Mis_Body_Acc_BC_(n)  (Eq. 11)

In an exemplary embodiment, all the acceleration vectors (e.g., but not limited to, Wind-Induced Acceleration, Gravity-Acceleration, and/or Missile Body Acceleration), may then be added in ECF to compute the Total Acceleration Vector in ECF, in block 338:

TAV_ECF_(n)=Mis_Acc_ECF_(n)+Wind_Acc_ECF_(n)+Gravity_Acc_ECF  (Eq. 12)

Once the Total Acceleration is calculated, it may be integrated into Velocity in ECF, in block 340, according to an exemplary embodiment:

Mis_Vel_ECF_(n+1)=Mis_Vel_ECF_(n)+TAV_ECF_(n) T  (Eq. 13)

Similarly, according to an exemplary embodiment, the integrate Velocity may be further integrated into Position in ECF, in block 342:

Mis_Pos_ECF_(n+1)=Mis_Pos_ECF_(n)+Mis_Vel_ECF_(n) T  (Eq. 14)

According to an exemplary embodiment, a new Missile Attitude may also be determined, in block 344:

E _(ECF) _(—) _(to) _(—) _(Missile,n+1)=DCM_XForm[{Act_Yaw_(n),Act_Pitch_(n),0]·E _(ECF) _(—) _(to) _(—) _(Missile,n)  (Eqs. 15)

Where  Act_Yaw  &  Act_Pitch  are  as  previously  defined: Act_Yaw_(n) = Act_Steer_BC_(n)[[1]] Act_Pitch_(n) = Act_Steer_BC_(n)[[2]]

Using the new Missile Attitude, in an exemplary embodiment, a new Missile Velocity Vector may be transformed from ECF to Missile Body Coordinates, in block 346:

Mis_Vel_BC_(n+1) =E _(ECF) _(—) _(to) _(—) _(Missile,n+1)·Mis_Vel_ECF_(n+1)  (Eq. 16)

In an exemplary embodiment, Range-To-Impact (RTI) calculation may be performed to determine the relative position of target with respect to the missile, in block 348:

Tx=Tgt_Pos_ECFn[[1]]

Ty=Tgt_Pos_ECFn[[2]]

Tz=Tgt_Pos_ECFn[[3]]

Mx=Mis_Pos_ECFn[[1]]

My=Mis_Pos_ECFn[[2]]

Mz=Mis_Pos_ECFn[[3]]

RTIn=Sqrt[(Tx−Mx)2+(Ty−My)2+(Tz−Mz)2]  (Eqs. 17)

Thereafter, in an exemplary embodiment, the Range-To-Impact Derivative (RTID_(n)=RTI_(n)−RTI_(n−1)) may be computed based on the RTI, in block 350. The RTID may be the indicator for the engagement closure state, with a negative RTID indicating “Closing” and a positive RTID indicating “Opening”. In an exemplary embodiment, for tail-aspect engagements, the closure state may initially be “Opening” as the missile accelerates off the launch rail, but may transition to “Closing” and remain there until the point of closest approach is reached. The process may end at B, in block 354, which is described with reference to FIG. 3C.

In FIG. 3C, starting with block 354, which corresponds to B in process 320, an exemplary embodiment may continue to compare the calculated RTID its previous value (RTID_(n) to RTID_(n−1)), block 362. In an exemplary embodiment, if a negative to positive transition has occurred, indicating a change in engagement closure state from “Closing” to “Opening”, it may be indicative that the missile has reached its closest point of approach sometime between time_(n) and time_(n−2). Thus, a determination may be made as to whether the missile has reached the point of closest approach based on a change in the engagement closure state, in block 364. If so, flow diagram 360 may continue with 366. In an exemplary embodiment, the aircraft state (x, y, z position and Yaw, Pitch, Roll attitude) and missile position (x, y, z) at time_(n) and time_(n−2) may be logged. Further, the process may continue with hit/miss assessment and/or damage assessment algorithm, which may determine where the missile has impacted the aircraft, and if so, where such impact has occurred, in block 366. The damage assessment algorithm may also determine if the missile has missed, but detonated the warhead within sufficient proximity to damage the aircraft.

In an exemplary embodiment, if no hit has occurred with the aircraft, a Terrain Hit/Miss assessment in block 366 and/or Terrain Impact computation may be performed, in block 368.

From 368, in an exemplary embodiment, a determination may be made as to whether the a terrain or the aircraft has been impacted, in block 370. If so, the flyout loop may be terminated and the impact event may be reported, in block 372.

If it is determined at block 364 that the missile has not reached the closest point of approach, or if it is determined at block 370 that the missile has not impacted a terrain or the target aircraft, a second determination may be made as to whether the maximum range of interest has been reached, in block 374. If so, the flyout loop may be terminated and the impact event may be reported, in block 372. Otherwise, the missile fly-out may continue with 322 until either the maximum range of interest is reached, or the missile impacts the target or the terrain, in block 374.

Exemplary Missile Guidance Processing

Exemplary Weapon (e.g., missile) Guidance Processing 204 is described herein for two exemplary missiles—the IR Seeker and the Laser Beam-Rider Guidance. It should be noted, however, that the Guidance Processing 204 is weapon specific. Thus, the two embodiments described herein are exemplary and should not be interpreted as limiting the present invention.

In an exemplary embodiment of the invention, for a missile with an IR seeker, the target position may be denoted as Aim-Point Error {Az,El} missile body coordinates. It may be assumed that variables and quantities computed as part of the Missile Kinematics Processing 202 are available to the seeker.

FIG. 4 illustrates an exemplary process 400 for a Weapon Guidance Processing 204 for an IR Seeker missile, according to an exemplary embodiment of the invention. In an exemplary embodiment, beginning with 402, the process 400 may obtain Target Position Vector and Missile Position Vector in ECF coordinates (Tgt_Pos_ECF and Mis_Pos_ECF, respectively), in block 404. The Relative Target Position may then be calculated relative to missile position in ECF by subtracting the two vector, in block 406, according to an exemplary embodiment:

Tgt_Rel_Pos_ECFn=Tgt_Pos_ECF−Mis_Pos_ECF  (Eq. 18)

The Relative Target Position, in an exemplary embodiment, may then be transformed into Missile Body Coordinates, in block 408:

Tgt_Rel_Pos_BCn=EECF_to_Missile,n·Tgt_Rel_Pos_ECF  (Eq. 19)

The {Az,El} vector to target (i.e., Aim-Point Error) may then be calculated, in block 410 according to an exemplary embodiment. The {x, y, z} below may be components of the Tgt_Rel_Pos_BC position vector.

El=ArcSin[−z]

Az=If[x>0,ArcSin[y/Cos [El]],If[y>0,Pi−ArcSin[y/Cos [El]],−Pi−ArcSin[y/Cos [El]]]]  (Eqs. 20)

From 410, in an exemplary embodiment, a determination may then be performed as to whether the gimbal limits has been exceeded, i.e., the Aim-point Error is greater than Gimbal_limit in either Az or El, in block 412. If so, in an exemplary embodiment, a Loss of Track event may be declared, the Aim-Point Error and Aim-Point Bias may be set to a static {0,0}, and the process may be held for the remainder of the missile flyout, in block 414. From 414, the process may then end, in block 420. If the gimbal limits are not exceeded, Aim-Point Bias (Static and Dynamic) may be added to the Aim-Point Error to compute Target Error, in block 416. In an exemplary embodiment, ±{Az, El} bias may be applied to account for missile aim-point lead or lag, or aim-point super-elevation or sub-elevation.

From 416, in an exemplary embodiment, the Required Steering Correction (Req_Steer_BC) may be computed using a Guidance Filter Difference Equation, in block 418. In an exemplary embodiment, the Difference Equation may be run on a per axis basis. From 418, the process may then end at 420.

FIG. 5 illustrates an exemplary Generalized Guidance Filter 500 implementing the Difference Equation. The exemplary Difference Equation of the Generalized Guidance Filter 500 may be as follows:

In=Target_Errorn

In−1=Target_Errorn−1

On−1=Req_Steer_BCn−1

α=(Kp+(Kd/T)+KiT)

β=(Kd/T)

On=αIn−βIn−1+On−1

Req_Steer_BCn=On  (Eqs. 21)

FIG. 6 illustrates an exemplary process 600 for a Weapon Guidance Processing 204 for a Laser Beam-Riding Seeker (RBS-70), according to an exemplary embodiment of the invention. For the RBS-70, the Aim-Point Error may be the {Az,El} laser orientation in missile body coordinates. In an exemplary embodiment, beginning with 602, the process 600 may get Laser Beam Unit Direction Vector in ECF coordinates (Laser_UDV_ECF), in block 604. The Laser Beam Unit Direction Vector may then be transformed to Laser Beam Vector in Missile Body Coordinates, in block 606:

Laser_UDV_BCn=EECF_to_Missile,n·Laser_UDV_ECF  (Eq. 22)

The {Az,El} Eulerians to Laser UDV (i.e., Aim-Point Error) may then be computed, in block 608. The {x, y, z} below may be components of the Laser_UDV_BC vector.

El=ArcSin[−z]

Az=If[x>0,ArcSin[y/Cos [El]],If[y>0,Pi−ArcSin[y/Cos [El]],−Pi−ArcSin[y/Cos [El]]]]  (Eqs. 23)

In an exemplary embodiment, a determination may then be performed as to whether the gimbal limits has been exceeded, i.e., the Aim-point Error is greater than Gimbal_limit in either Az or El, in block 610. If so, in an exemplary embodiment, a Loss of Track event may be declared, the Aim-Point Error and Aim-Point Bias may be set to a static {0,0}, and the process may be held for the remainder of the missile flyout, in block 612. From 612 the process may then end, in block 618.

Otherwise, Aim-Point Bias (Static and Dynamic) may be added to the Aim-Point Error to compute Target Error, in block 614. In an exemplary embodiment, ±{Az, El} bias may be applied to account for missile aim-point lead or lag, or aim-point super-elevation or sub-elevation. In an exemplary embodiment, the Required Steering Correction (Req_Steer_BC) may then be computed, as detailed above for the IR Seeker, in block 616. From 616, the process 600 may then end at 618.

Exemplary Computational Details for DCM from {Yaw, Pitch, Roll} Eulerian

In an exemplary embodiment, Direction Cosine Matrix may be a 3×3 Matrix used to transform coordinates (vectors) between reference frames. The exemplary DCM transform may be computed as follows:

$\begin{matrix} {{{DCM\_ XForm}\left\lbrack \left\{ {{yaw\_},{pitch\_},{roll\_}} \right\} \right\rbrack}:=\left\{ {\left\{ {{{{Cos}\lbrack{yaw}\rbrack}{{Cos}\lbrack{pitch}\rbrack}},{{{Sin}\lbrack{yaw}\rbrack}{{Cos}\lbrack{pitch}\rbrack}},{- {{Sin}\lbrack{pitch}\rbrack}}} \right\},\left\{ {{{{- {{Sin}\lbrack{yaw}\rbrack}}{{Cos}\lbrack{roll}\rbrack}} + {{{Cos}\lbrack{yaw}\rbrack}{{Sin}\lbrack{pitch}\rbrack}{{Sin}\lbrack{roll}\rbrack}}},{{{{Cos}\lbrack{yaw}\rbrack}{{Cos}\lbrack{roll}\rbrack}} + {{{Sin}\lbrack{yaw}\rbrack}{{Sin}\lbrack{pitch}\rbrack}{{Sin}\lbrack{roll}\rbrack}}},{{{Cos}\lbrack{pitch}\rbrack}{{Sin}\lbrack{roll}\rbrack}}} \right\},\left\{ {{{{{Sin}\lbrack{yaw}\rbrack}{{Sin}\lbrack{roll}\rbrack}} + {{{Cos}\lbrack{yaw}\rbrack}{{Sin}\lbrack{pitch}\rbrack}{{Cos}\lbrack{roll}\rbrack}}},{{{- {{Cos}\lbrack{yaw}\rbrack}}{{Sin}\lbrack{roll}\rbrack}} + {{{Sin}\lbrack{yaw}\rbrack}{{Sin}\lbrack{pitch}\rbrack}{{Cos}\lbrack{roll}\rbrack}}},{{{Cos}\lbrack{pitch}\rbrack}{{Cos}\lbrack{roll}\rbrack}}} \right\}} \right\}} & \left( {{Eq}.\mspace{14mu} 24} \right) \end{matrix}$

A DCM may have an intrinsic directionality. For example, if the DCM is defined to describe missile orientation with respect to the ECF, its sense of direction may be from the ECF to the Missile Body Coordinate Frame. A Vector may be transformed from the ECF to missile body coordinates by pre-multiplying by the DCM:

Vector_BC=DCM·Vector_ECF  (Eq. 25)

To go the other direction, a vector in missile body coordinates can be pre-multiplied by the “Transpose” of the DCM:

Vector_ECF=Transpose[DCM]·Vector_BC  (Eq. 26)

Exemplary Computational Details for Wind-Induced Acceleration in ECF

In an exemplary embodiment, acceleration due to wind may be taken as a magnitude of K_(w)V_(w) ²A, in the direction of the wind, where A is the projected area in the direction of the wind, found by taking the vector dot product of the missile Area Vector onto a Unit Direction Vector indicating wind direction:

Wind_Mag_Sq=Wind_Vel_ECF·Wind_Vel_ECF (Vector Dot Product)

Wind_Mag=Sqrt[Wind_Mag_Sq]

Wind_Dir_ECF=Wind_Vel_ECF/Wind_Mag (Unit Dir. Vector)

Area_Proj=Area_Vec·Wind_Dir_ECF (Vector Dot Product)

Wind_Acc_Mag=KwWind_Mag_Sq Area_Proj (Scalar Multiply)

Wind_Acc_ECF=Wind_Acc_Mag Wind_Dir_ECF (Scalar×Unit Vector)  (Eqs. 27)

Exemplary Computational Details for Application of Acceleration Limits to Missile Steering

In an exemplary embodiment, the Required Steering Vector may exceed the maneuverability limits of the missile, as specified by the G_limit parameter. The Actual Steering Vector may therefore be an acceleration-restricted version of the Required Steering Vector.

In an exemplary embodiment, at time t_(n), the missile has a velocity, in body coordinates, of Mis_Vel_BC_(n). This velocity may be aligned with the missile x-axis, though it may not to be aligned exactly on it. Thus, it may be needed to compute the velocity magnitude:

Mis_Vel_MagSqn=Mis_Vel_BCn·Mis_Vel_BCn (Vector Dot Product)

Mis_Vel_Magn=Sqrt[Mis_Vel_MagSqn]  (Eqs. 28)

The Required Steering Vector (Req_Steer_BC) may be a {Yaw, Pitch} Eulerian:

Req_Yawn=Req_Steer_BCn[[1]]

Req_Pitchn=Req_Steer_BCn[[2]]  (Eqs. 29)

The rate of turn (Angular limit per update) may be inversely proportional to the magnitude of velocity, and computed as follows:

Angle_Limitn=ArcSin[(TG_Acc_Scalar G_limit)/Mis_Vel_Magn]  (Eq. 30)

The Actual Steering Vector may be limited to have both Yaw and Pitch with the ±Angle Limit:

Act_Yawn=If[Req_Yawn>Angle_Limitn,Angle_Limitn,If[Req_Yawn<=Angle_Limitn,−Angle_Limitn,Req_Yawn]]

Act_Pitchn=If[Req_Pitchn>Angle_Limitn,Angle_Limitn,If[Req_Pitchn<−Angle_Limitn,−Angle_Limitn,Req_Pitchn]]

Act_Steer_BCn={Act_Yawn,Act_Pitchn}  (Eqs. 31)

Exemplary Computational Details for Missile Body Accelerations Due to Steering

When the missile is steered, accelerations result due to changes in velocity. Since the steering occurs in body coordinates, these accelerations may be computed in body coordinates, then transformed into the ECF for integration into velocity and position.

Rotated_Mis_Vel_BCn=DCM_XForm[{Act_Yawn,Act_Pitchn,0}]·Mis_Vel_BCn

Mis_Steer_Acc_BCn=(Rotated_Mis_Vel_BCn−Mis_Vel_BCn)/T  (Eqs. 32)

Exemplary Hit/Miss Assessment

According to an exemplary embodiment of the invention, in order to resolve the issues pointed out with the conventional simulation models caused by high rates of weapon and target speed, the Hit/Miss assessment may be performed on the Aircraft Body Coordinate Frame.

In conventional assessment modeling, at some time (t₀), both the aircraft and weapon would have an instantaneous position in a common frame of reference, e.g., but not limited to, the Engagement Coordinate Frame (ECF), which is an earth-fixed coordinate frame. At the time increment following the point of closest approach (t₂), both aircraft and weapon would have a new position. However, due to the rate of speed of both the weapon and the target aircraft, the two could have easily flown through one other, leaving the instant of collision undetected.

Accordingly, in an exemplary embodiment of the invention, in order to ensure that a miss is not undetected, the weapon position may be mathematically transformed from the fixed Engagement Coordinate Frame (ECF) to the Aircraft Body Coordinate Frame. In an exemplary embodiment, performing this transformation may express the weapon position with respect to a set of coordinates that are fixed to the aircraft. When both the weapon position at time t₀ (time_(n−2)) and time t₂ (time_(n)) are transformed into aircraft coordinates, we are left with two points in aircraft coordinate space. In an exemplary embodiment, these two points may be separated in time by, e.g., but not limited to, 66.000 ms, where the weapon is known to have been located with respect to the target aircraft.

According to an exemplary embodiment of the invention, if a straight line between these two locations passes through one of the ellipsoid surfaces that comprise the aircraft interference model, as described above, it may be determined that a trajectory of the weapon has made impact with the aircraft. In an exemplary embodiment, the ellipsoid that has been intersected may represent the section of the aircraft that has been damaged, and the coordinates of the intersection may represent the coordinates at which a hit has occurred.

FIG. 7 demonstrates an exemplary Hit/Miss Assessment process 700 for a target aircraft, according to an exemplary embodiment of the invention. The process 700 may begin at 702 and may continue with modeling the target aircraft interference geometry, in block 704. In an exemplary embodiment, the aircraft may be modeled as, e.g., but not limited to, 10 zones. In an exemplary embodiment, each zone (ellipsoid) may be defined by the following set of 9 parameters:

-   -   {a, b, c, x₀, y₀, z₀, zone_yaw, zone_pitch, zone_roll}         where the “zone_” prefix denotes the yaw, pitch, or roll of the         specific ellipsoidal zone.

In an exemplary embodiment, the determination of Hit/Miss Assessment on the target plane may be defined by two samples in time, in which both the aircraft and the weapon are in motion with respect to the Engagement Coordinate Frame (ECF). Thus, from 704, the process 700 may continue with determining the aircraft and weapon coordinates in the ECF, in block 706. In an exemplary embodiment, the two time samples, t_(n) and t_(n−2) may bracket the point of closest approach. Exemplary parameters to determine the aircraft and weapon (e.g., missile) coordinates are as follows:

AC_Pos_ECF₀={x,y,z} aircraft position vector in ECF at time t_(n−2)

AC_Pos_ECF₂={x,y,z} aircraft position vector in ECF at time t_(n)

AC_Att_ECF₀={Yaw,Pitch,Roll} aircraft attitude vector in ECF at time t_(n−2)

AC_Att_ECF₂={Yaw,Pitch,Roll} aircraft attitude vector in ECF at time t_(n)

Mis_Pos_ECF₀={x,y,z} missile position vector in ECF at time t_(n−2)

Mis_Pos_ECF₂={x,y,z} missile position vector in ECF at time t_(n)

In an exemplary embodiment, after determining weapon and aircraft coordinates in the ECF, the weapon coordinates may be transformed to Aircraft Body Coordinate Frame, in block 708. The weapon position relative to the aircraft in the ECF, at both points in time, t_(n) and t_(n−2), may be calculated by subtracting the Aircraft position vectors from the Weapon Position vectors in the ECF. Weapon position in Aircraft Body Coordinates (ACBC) may then be found by transforming the relative weapon coordinates from the ECF to the ACBC. Exemplary formulas for performing this transformation are as follows:

Mis_Rel_Pos_ECF0=Mis_Pos_ECF0−AC_Pos_ECF0

Mis_Rel_Pos_ECF2=Mis_Pos_ECF2−AC_Pos_ECF2  (Eq. 33)

E_(ECF) _(—) _(to) _(—) _(AC,0)=DCM_XForm[AC_Att_ECF₀]

E_(ECF) _(—) _(to) _(—) _(AC,2)=DCM_XForm[AC_Att_ECF₂]  (Eq. 34)

Mis_Rel_Pos_ACBC₀ =E _(ECF) _(—) _(to) _(—) _(AC,0)·Mis_Rel_Pos_ECF₀

Mis_Rel_Pos_ACBC₂ =E _(ECF) _(—) _(to) _(—) _(AC,2)·Mis_Rel_Pos_ECF₂  (Eq. 35)

In an exemplary embodiment, as described above, each aircraft zone may include its own attitude defined by zone_yaw, zone_pitch, and zone_roll parameters. The ellipsoid al zone may be rotated from aircraft coordinates by the zone_yaw, zone_Pitch, and zone_roll parameters. Thus, in an exemplary embodiment, the relative weapon coordinates in ACBC may be transformed to get the trajectory points of the weapon with relative to the aircraft zones in the Aircraft Zone Coordinates, in block 710. Exemplary formulas for performing this transformation are as follows:

E_(AC) _(—) _(to) _(—) _(zone)=DCM_XForm[{zone_yaw,zone_pitch,zone_roll}]  (Eq. 36)

Mis_Rel_Pos_ACZC₀ =E _(AC) _(—) _(to) _(—) _(zone)·Mis_Rel_Pos_ACBC₀

Mis_Rel_Pos_ACZC₂ =E _(AC) _(—) _(to) _(—) _(zone)·Mis_Rel_Pos_ACBC₂  (Eq. 37)

Once the weapon coordinates have been determined with respect to the ellipsoidal zones, a determination may be made as to whether a zone of the aircraft intercepts the weapon trajectory, in block 712. If an intercept occurs, it may be determined that the aircraft has been hit, in block 714. Otherwise, it may be determined that the weapon ha missed the aircraft, in block 716.

In a further exemplary embodiment, if it is determined that a hit has occurred (i.e., Hit=True), from 714 the impact coordinates may then be computed, in block 718. Further, from 718 the damage caused by the weapon on the aircraft may also be assessed, in block 720 before ending with 726.

Similarly, if it is determined that the elliptical zone was not impacted (i.e., Hit=False), from 716 the distance by which the weapon missed the aircraft may be calculated, in block 722. Further, while the weapon does not actually impact the aircraft, if the aircraft is within a blast range of the weapon warhead, the aircraft may still be damaged. Thus, the proximity damage of the aircraft may be assessed, in block 724. These steps will be discussed later in great detail. From 724, process 700 may end at 726.

Referring now to FIG. 8, an exemplary process 800 for determining whether a zone of the aircraft intercepts the weapon trajectory (block 712 of FIG. 7) is illustrated according to an exemplary embodiment of the invention. Process 800 may start at 802 and may continue with determining a parametric expression for a line-segment through the two trajectory points in zone coordinates, in block 804. This parametric expression may be needed to determine whether an intercept occurs. Exemplary parametric expressions are as follows:

S=Mis_Rel_Pos_ACZC₂−Mis_Rel_Pos_ACZC₀

x=S[[1]]; Sy=S[[2]]; Sz=S[[3]]

0x=Mis_Rel_Pos_ACZC₀[[1]]

P0y=Mis_Rel_Pos_ACZC₀[[2]]

P0z=Mis_Rel_Pos_ACZC₀[[3]]

x=P0x+iSx

y=P0y+iSy

z=P0z+iSz  (Eqs. 38)

The x, y, and z parameters listed above may form a parametric vector trajectory connecting the two weapon relative position points. In the exemplary embodiment shown, when i=0, the position is Mis_Rel_Pos_ACZC₀, and when i=1, the position is Mis_Rel_Pos_ACZC₂. At some point between i=0 and i=1, the trajectory may pass through the ellipsoid or reach a point of closest approach.

From 804, in an exemplary embodiment, the point of closest approach may be calculated, in block 806. The exemplary closed-form solution to the value of i that represents the point of closest approach is as follows:

$\begin{matrix} {{iSolution} = \frac{- \left( {{b^{2}c^{2}P\; 0{xSx}} + {a^{2}c^{2}P\; 0{ySy}} + {a^{2}b^{2}P\; 0{zSz}} - {b^{2}c^{2}{{Sx} \cdot x}\; 0} - {a^{2}c^{2}{{Sy} \cdot y}\; 0} - {a^{2}b^{2}{{Sz} \cdot z}\; 0}} \right)}{{b^{2}c^{2}{Sx}^{2}} + {a^{2}c^{2}{Sy}^{2}} + {a^{2}b^{2}{Sz}^{2}}}} & \left( {{Eq}.\mspace{14mu} 39} \right) \end{matrix}$

From 806, after calculating the point of closest approach, according to an exemplary embodiment, an Elliptical Magnitude may be computed at the point of closest approach, in block 808. In an exemplary embodiment, the Elliptical Magnitude (EMag) for the zone may be defined as follows:

$\begin{matrix} {{EMag} = {{\frac{\left( {x - {x\; 0}} \right)^{2}}{a^{2}} + \frac{\left( {y - {y\; 0}} \right)^{2}}{b^{2}} + \frac{\left( {z - {z\; 0}} \right)^{2}}{c^{2}}} = 1}} & \left( {{Eq}.\mspace{14mu} 40} \right) \end{matrix}$

By definition, the surface of the ellipsoid is the locus of points for which the EMag function is equal to 1. Therefore, in an exemplary embodiment, in 810 if the EMag function at the point of closest approach is less than 1, it may be determined that the surface has been struck, in block 812. Otherwise, if PCA is not less than 1 in 810, then it may be determined that the projectile has missed, in block 814. From 812 and 814, process 800 may then end at block 816.

In an exemplary embodiment, the determination may be made by evaluating EMag at the {x,y,z} values produced by setting i equal to iSolution, as follows:

Hit=If[(EMag/·i->iSolution)<1,True,False]  (Eq. 41)

Exemplary Computation of Impact Coordinates

According to an exemplary embodiment of the invention, if the impact has occurred (i.e., Hit=True), the impact coordinates of the weapon may be computed, as previously discussed briefly. In an exemplary embodiment, the impact coordinates may be computed in the Aircraft Zone Coordinate System by evaluating the parametric trajectory at i=iSolution, as follows:

Hit_Loc_ACZC={x,y,z}/·i->iSolution  (Eq. 42)

In a further exemplary embodiment, the impact location in Aircraft Body Coordinates may be found by rotating the Hit Location coordinates from the Aircraft Zone Coordinates (ACZC) to the aircraft body coordinates (ACBC), as follows:

Hit_Loc_ACBC=Transpose[E_(AC) _(—) _(to) _(—) _(zone)]·Hit_Loc_ACZC  (Eq. 43)

Exemplary Miss Distance Computation

In an exemplary embodiment, if the ellipsoidal zone was not impacted (Hit=False), the distance by which the weapon missed the aircraft may be computed, as previously discussed briefly. In Aircraft Zone Coordinates, as described with reference to block 804 of FIG. 8 and Eqs. 38, the following may represent the relation for the trajectory segment:

S1=S=Mis_Rel_Pos_ACZC₂−Mis_Rel_Pos_ACZC₀  (Eq. 44)

Also, in Aircraft Zone Coordinates, the centroid of the ellipsoid resides at C={x₀, y₀, z₀}. Thus, the distance of the first trajectory point with respect to the centroid may be computed as:

S2=Mis_Rel_Pos_ACZC₀ −C  (Eq. 45)

In an exemplary embodiment, the miss-distance may be computed using vector mathematics and the distances S1, S2. To do so, in an exemplary embodiment, two orthogonal vectors may be defined. The first orthogonal vector (Ortho1) may be found by taking the vector cross product of S2 into S1. This creates a vector that is perpendicular to the plane that contains both the trajectory and Point C. The second orthogonal vector (Ortho2) may be found by taking the vector cross product of S1 into Ortho1. This creates a vector that is perpendicular to both the trajectory and Ortho1, which means that it is both perpendicular to the trajectory and it lies in the plane that contains both the trajectory and Point C. Thus, Ortho 2 indicates the direction of line running from the centroid of the ellipsoidal zone (Point C) that will intersect the trajectory at right angles.

Ortho1=(S2×S1)

Ortho2=(S1×Ortho1)  (Eqs. 46)

In an exemplary embodiment, to determine the miss distance, the magnitude of Ortho 2 may be scaled to unity to obtain a Unit Direction Vector (UDV). Then, to compute a vector from Point C to the trajectory of closest point of approach (i.e., Miss Vector) by computing the vector projection (i.e., dot product) of vector S2 onto the UDV. The magnitude of the Miss Vector is the miss distance. Exemplary equations for performing this computation is as follows:

Ortho2Mag=Sqrt[Ortho2·Ortho2] (Magnitude of Ortho 2)

Ortho2UDV=Ortho2/Ortho2Mag (Unit Direction Vector)

Miss_Vec=S2·Ortho2UDV

Miss_Dist=Sqrt[Miss_Vec·Miss_Vec]  (Eqs. 47)

In an exemplary embodiment, the coordinates of the point of closest approach (e.g., Miss Coordinates) may be computed in Aircraft Zone Coordinates as follows:

Miss_Loc_ACZC=Miss_Vec+C  (Eq. 48)

Further, in an exemplary embodiment, the miss location in Aircraft Body Coordinates may be computed by rotating the Miss Coordinates from the Aircraft Zone Coordinates (ACZC) to the Aircraft Body Coordinates (ACBC), as follows:

Miss_Loc_ACBC=Transpose[E_(AC) _(—) _(to) _(—) _(Zone)]·Miss_Loc_ACZC  (Eq. 49)

Exemplary Impact Damage Assessment

In an exemplary embodiment, if an impact occurs, the damage on the aircraft may be computed from a statistical model that considers factors such as, e.g., but not limited to, weapon lethality, the survivability of the target aircraft, and the location of impact on the aircraft. In an exemplary embodiment, where there are multiple hits on the aircraft, damage may be integrated from each hit until a survivability threshold is reached, at which time the target is considered “Killed”.

In an exemplary embodiment, the overall damage model has the following components:

Weapon Lethality (Property of Weapon) Target Survivability (Property of Aircraft) Zone Sensitivity (Property of Aircraft Zones)

In an exemplary embodiment, Weapon Lethality may specify the single-shot, direct impact, potency of the weapon. Weapon Lethality may be measured in Damage Units. In an exemplary embodiment, the assumed reference for Damage Units may be, for example, that 100 Damage Units are required to Kill a Fast Jet. Weapon Lethality may be modeled as Log-Normal probability distribution, in which the Mean (μ) and Standard Deviation (σ) may be user-configurable model parameters.

In an exemplary embodiment, for each hit, a random draw may be taken from a probability distribution function to determine the number of Damage Units resulting from that hit. Damage Units may be integrated from multiple hits, across all zones, to assess the overall damage state of the aircraft.

In an exemplary embodiment, the lethality of different weapons may be modeled by assigning appropriate Mean and Standard Deviation parameters for each weapon. For example, a single 35 mm shell may have a Mean of 20 Damage Units, with a Standard Deviation of 10. Thus, on average, 5 hits of a 35 mm shells would be needed to take down a Fast Jet, though more or fewer number of shots may be needed. For example, 3 “lucky shots” may be able to kill a Fast Jet.

Alternatively, the RBS-70 Warhead is so potent that it might be modeled with a Mean of 1000 Damage Units, and Standard Deviation of 70, if the warhead detonates. With such a model there is unity probability that a hit with a RBS-70 warhead would bring down a Fast Jet on impact, and a significant probability of kill at a 10 meter miss distance (as discussed below). However, if the RBS-70 warhead fails to detonate, e.g., due to warhead malfunction, the impact damage might be modeled as a Mean of 100 Damage Units, with a Standard Deviation of 50. Thus, if the exemplary RBS-70 fails to detonate, it might or might not take down the aircraft, due to the force of collision alone.

In an exemplary embodiment, the Target Survivability component is the number of Damage Units that a target can sustain before it is killed. In an exemplary embodiment, each type of aircraft may be modeled with a representative Survivability Threshold, and when the integrated damage exceeds this threshold, the target may be considered to be “killed”. In an exemplary embodiment, the defined reference benchmark for Survivability Threshold may be 100 Damage Units to kill a Fast Jet. Sturdier targets (e.g., Large Propeller Aircraft) may be modeled with a higher threshold, while more vulnerable targets (e.g., helicopter) may be modeled with a lower threshold. In an exemplary embodiment, survivability threshold, in Damage Units, is a user-configurable model parameter.

In an exemplary embodiment, Zone Sensitivity may include a set of user-configurable model parameters. Each of the ellipsoidal zones used to form the Target Interference Geometry, as previously discussed, may have a Sensitivity Coefficient, an exemplary embodiment of which is illustrated in Table 8 below:

TABLE 8 Example Proximity Zone Sensitivity Model (Fast Jet Aircraft) SENSITIVITY ZONE DESCRIPTION COEFFICIENT 1 Forward Fuselage 1.5 2 Aft Fuselage 2 3 Left Wing 0.7 4 Right Wing 0.7 5 Left Rear Stabilizer 0.7 6 Right Rear Stabilizer 0.7 7 Vertical Stabilizer 0.7

In an exemplary embodiment, the sensitivity coefficients may provide a mechanism to account for the fact that all areas of the aircraft are not equally sensitive to damage. For example, a non-explosive bullet may cause relatively little damage if it impacts a wing, but a great deal of damage if it impacts the center fuselage, where the jet turbines reside. In an exemplary embodiment, the sensitivity coefficients may be used as “weighting factors” that adjust the damage levels resulting from different regions of impact.

Referring now to FIG. 9, an exemplary process 900 for calculating the aircraft damage assessment is described, according to an exemplary embodiment of the invention. In an exemplary embodiment, the process 900 may start at 902, in which the aircraft has zero initial damage (AC_Damage₀=0). When a weapon has been determined to have passed the point of closest approach, the process 900 may follow to determine if zone has been hit (as discussed with reference to FIG. 4), in block 904. If so, the process 900 may follow to 906 to continue to make a random draw from the probability distribution function of the appropriate Weapon Lethality model, in block 906. The exemplary equation for making a random draw for Weapon Lethality may be as follows:

Weap_Lethality=LogNormalRandom[μ,σ]  (Eq. 50)

Thereafter, from 906, in an exemplary embodiment, Weapon Lethality may be multiplied by Zone Sensitivity to determine effective lethality of the weapon on the target aircraft, in block 908, as follows:

Effective_Lethality=Weap_Lethality×Sensitivity_Coeff  (Eq. 51)

The Effective Lethality of the weapon on the aircraft may then be integrated into the existing damage on the aircraft, in block 910, as follows:

AC_Damage_(n+1)=AC_Damage_(n)+Effective_Lethality  (Eq. 52)

Thereafter, in 912 a determination may be made as to whether the total damage on the aircraft exceeds its Survivability Threshold, which may indicate that the Aircraft has been killed, in block 912. This “Test for Kill” may be determined as follows:

Kill=If[AC_Damage>Survivability_Threshold,True,False]  (Eq. 53)

From 912 flow diagram 900 may end with 914.

Exemplary Proximity Damage Assessment

According to an exemplary embodiment of the invention, if the missile does not actually impact the aircraft, but the closest point of approach is within the blast range of a missile warhead, the aircraft may still be damaged. For proximity damage, in an exemplary embodiment, the warhead lethality model described above may be weighted with a range term, to account for energy loss as a function of miss distance.

The energy from weapon explosion may be modeled as a sphere. Energy from an expanding sphere dissipates according to 1/R². If the warhead uses a shaped charge different from a spear, e.g., but not limited to, to form an annular ring, the dissipation function may be closer to, e.g., but not limited to, 1/R or 1/R^(1.2). To account for these possibilities, the exemplary parametric model for the warhead may include a user definable coefficient (e.g., Warhead_n), that represents the exponent in the proximity propagation function.

In an exemplary embodiment, proximity damage may be modeled similarly to the impact damage model, with the addition of a factor for Range Loss. Referring back to FIG. 9, when a weapon has been determined to have passed the point of closest approach, but the determination in 904 indicates that the zone has not been hit, then flow diagram 900 may continue with 914, each zone of the aircraft may be assessed for damage from a proximity detonation, unless the weapon malfunctions or fails to detonate.

In an exemplary embodiment, the process 900 in such scenario may continue to compute the miss distance to zone centroid, as was discussed previously, in block 914. From 914, the Range Loss may then be computed at the computed miss distance, in block 916, as follows:

Range_Loss=(Miss_Dist+1)^(−Warhead) ^(—) ^(n)  (Eq. 54)

Thereafter, from 916, a random draw may be made from the probability distribution function of the appropriate Weapon Lethality model, as shown in Eq. 27, in block 918. From 918, the Weapon's Effective Lethality may then be calculated by multiplying the Weapon Lethality by Zone Sensitivity and Range Loss, in block 920, as follows:

Effective_Lethality=Weap_Lethality×Sensitivity_Coeff×Range_Loss  (Eq. 55)

The process 900 from 920 may then follow to blocks 910, and 912, where aircraft damage may be integrated and the test for kill may be performed and may complete with 914.

In an exemplary embodiment, proximity damage may only apply to weapons with explosive warheads. In an exemplary embodiment, the same model may be used for non-explosive weapons, e.g., but not limited to, bullet, but the “Warhead_n” parameter may be set to a large value (e.g., but not limited to, 1000) to effectively disable any proximity damage effect.

Exemplary Weapon Data

The listings below summarize exemplary parameters of the weapon systems. It should be noted that these parameters are for illustration purposes only and may not accurately represent the actual weapon parameters. Also, it should be understood that the present invention is by no means limited to the weapons listed herein.

BOFORS RBS-70 Basic Laser-Guided SAM, reportedly virtually smokeless. Can Description: be in either of 2 configurations: Mounted on V200 AFV, or dismounted on Tripod. Manufacturer claims “unique unjammable laser beam riding guidance” provides high capability against small targets such cruise missiles & UAVs Weight: 87 Kg Missile 1.735 m Length: Missile 152 mm Diameter: Dia with 320 mm wings open: Warhead: 1.8 Kg shaped charge & fragmentation Fusing: Adaptive Proximity Fuse or impact Speed: Mach 2 (660 m/s) Flight time 8.5 sec to 3 Km: Effective Up to 3 Km Altitude: Effective 0.3 to 5 Km Range: Guidance: Laser beam-rider Normal Monocular telescope, 7× magnification, 9° FOV Sight: Thermal IR Image, 1× mag, 9.15° H × 6.86° V FOV (±2%) Sight:

MATRA Mistral Basic Description: IR-Homing MANPADS, manufactured by MBDA (French) Launch Mass: 18.7 Kg Power Plant: two-stage solid rocket Length: 1.86 m Missile Caliber: 90 mm Dia with wings open: 180 mm Warhead: 3 Kg HE Fusing: Laser Proximity or impact Speed: Mach 2.5 (830 m/s) Flight time to 3 Km: 5.2 sec Max Flight Time: 14 sec Effective Altitude: up to 3 Km Effective Range: 0.5-5.5 Km (4 Km against helicopters) Max Range: 6.5 km Acquisition Sight: Clear Collimator, ±25° H × ~15° V FOV Magnifying Sight: 3× magnification, 14° FOV Guidance: All-aspect IR, fire and forget

KBM SA-18 IGLA (Grouse) Basic Russian IR-Homing MANPADS, similar to Description: Stinger, manufactured by KBM. Can be used in either of two configurations (MANPADS Shoulder Launch, or M113-mounted) Launch 10.6 Kg Mass: Length: 1.7 m Missile 72 mm Caliber: Dia with 180 mm wings open: Warhead: 1.27 Kg HE Fusing: Laser Proximity or impact Speed: Mach 1.7 (570 m/s) Effective 10 m to 2 Km (FWA) or 3 KM (RWA) Altitude: Effective 0.5-2 Km (FWA) or 5.2 Km (RWA) Range: Manpads STIS Staring IR Image, 9° × 9° FOV Accessory Sight: M113 DNSS Wide FOV: 9°, 3× Mag Day Channel: Narrow FOV: 2°, 15× Mag M113 DNSS 2°, 1× Mag2°, 15× Mag Night Channel: Guidance: All-aspect IR with proportional convergence, fire and forget

OERLIKON-CONTRAVES Twin 35 mm AA Guns Basic Description: Swiss AAA twin barrel gun for rapid fire of unguided projectiles. Projectile Mass: 550 g Rate of Fire: 1100 rounds/min (550 from each of 2 barrels) Muzzle Velocity: 1175 m/s Flight Time: 1000 m: 0.96 Sec 2000 m: 2.18 Sec 3000 m: 3.80 Sec 4000 m: 6.06 Sec (up to 111 rounds in air) Magazine: 112 Ready; 126 Reserve; 238 total Effective Altitude: 3 Km Max Effective Range: 4 Km Manual Fire Control: I ron Sight Radar Fire Control: Closed-Loop automated fire control solution from Super Fledermaus Pulse Doppler radar

Exemplary Embodiment of Computer Environment

FIG. 10 depicts an exemplary computer system that may be used in implementing an exemplary embodiment of the present invention. Specifically, FIG. 10 depicts an exemplary embodiment of a computer system 1000 that may be used in computing devices such as, e.g., but not limited to, a client and/or a server, etc., according to an exemplary embodiment of the present invention. FIG. 10 depicts an exemplary embodiment of a computer system that may be used as client device 1000, or a server device 1000, etc. The present invention (or any part(s) or function(s) thereof) may be implemented using hardware, software, firmware, or a combination thereof and may be implemented in one or more computer systems or other processing systems. In fact, in one exemplary embodiment, the invention may be directed toward one or more computer systems capable of carrying out the functionality described herein. An example of a computer system 1000 may be shown in FIG. 10, depicting an exemplary embodiment of a block diagram of an exemplary computer system useful for implementing the present invention. Specifically, FIG. 10 illustrates an example computer 1000, which in an exemplary embodiment may be, e.g., (but not limited to) a personal computer (PC) system running an operating system such as, e.g., (but not limited to) MICROSOFT® WINDOWS® NT/98/2000/XP/CE/ME/VISTA/etc. available from MICROSOFT® Corporation of Redmond, Wash., U.S.A. However, the invention may not be limited to these platforms. Instead, the invention may be implemented on any appropriate computer system running any appropriate operating system. In one exemplary embodiment, the present invention may be implemented on a computer system operating as discussed herein. An exemplary computer system, computer 1000 may be shown in FIG. 10. Other components of the invention, such as, e.g., (but not limited to) a computing device, a communications device, mobile phone, a telephony device, a telephone, a personal digital assistant (PDA), a personal computer (PC), a handheld PC, an interactive television (iTV), a digital video recorder (DVD), client workstations, thin clients, thick clients, proxy servers, network communication servers, remote access devices, client computers, server computers, routers, web servers, data, media, audio, video, telephony or streaming technology servers, etc., may also be implemented using a computer such as that shown in FIG. 10. Services may be provided on demand using, e.g., but not limited to, an interactive television (iTV), a video on demand system (VOD), and via a digital video recorder (DVR), or other on demand viewing system.

The computer system 1000 may include one or more processors, such as, e.g., but not limited to, processor(s) 1004. The processor(s) 1004 may be connected to a communication infrastructure 1006 (e.g., but not limited to, a communications bus, cross-over bar, or network, etc.). Various exemplary software embodiments may be described in terms of this exemplary computer system. After reading this description, it may become apparent to a person skilled in the relevant art(s) how to implement the invention using other computer systems and/or architectures.

Computer system 1000 may include a display interface 1002 that may forward, e.g., but not limited to, graphics, text, and other data, etc., from the communication infrastructure 1006 (or from a frame buffer, etc., not shown) for display on the display unit 1030.

The computer system 1000 may also include, e.g., but may not be limited to, a main memory 1008, such as, e.g., but not limited to, a random access memory (RAM), and a secondary memory 1010, etc. The secondary memory 1010 may include, for example, (but not limited to) a hard disk drive 1012 and/or a removable storage drive 1014, representing a floppy diskette drive, a magnetic tape drive, an optical disk drive, a compact disk drive CD-ROM, etc. The removable storage drive 1014 may, e.g., but not limited to, read from and/or write to a removable storage unit 1018 in a well known manner. Removable storage unit 1018, also called a program storage device or a computer program product, may represent, e.g., but not limited to, a floppy disk, magnetic tape, optical disk, compact disk, etc. which may be read from and written to by removable storage drive 1014. As may be appreciated, the removable storage unit 1018 may include a computer usable storage medium having stored therein computer software and/or data. In some embodiments, a “machine-accessible medium” may refer to any storage device used for storing data accessible by a computer. Examples of a machine-accessible medium may include, e.g., but not limited to: a magnetic hard disk; a floppy disk; an optical disk, like a compact disk read-only memory (CD-ROM) or a digital versatile disk (DVD); a magnetic tape; and a memory chip, etc.

In alternative exemplary embodiments, secondary memory 1010 may include other similar devices for allowing computer programs or other instructions to be loaded into computer system 1000. Such devices may include, for example, a removable storage unit 1022 and an interface 1020. Examples of such may include a program cartridge and cartridge interface (such as, e.g., but not limited to, those found in video game devices), a removable memory chip (such as, e.g., but not limited to, an erasable programmable read only memory (EPROM), or programmable read only memory (PROM) and associated socket, and other removable storage units 1022 and interfaces 1020, which may allow software and data to be transferred from the removable storage unit 1022 to computer system 1000.

Computer 1000 may also include an input device 1016 such as, e.g., (but not limited to) a mouse or other pointing device such as a digitizer, and a keyboard or other data entry device.

Computer 1000 may also include an output device such as, e.g., (but not limited to) display 1030, and display interface 1002. The computer 1000 may also include other output devices 1030 such as, e.g., but not limited to, a printer.

Computer 1000 may include other input/output (I/O) devices such as, e.g., (but not limited to) communications interface 1024, cable 1028 and communications path 1026, etc. These devices may include, e.g., but not limited to, a network interface card, and modems (neither are labeled). Communications interface 1024 may allow software and data to be transferred between computer system 1000 and external devices.

In this document, the terms “computer program medium” and “computer readable medium” may be used to generally refer to media such as, e.g., but not limited to removable storage drive 1014, a hard disk installed in hard disk drive 1012, and signals 1028, etc. These computer program products may provide software to computer system 1000. The invention may be directed to such computer program products.

References to “one embodiment,” “an embodiment,” “example embodiment,” “various embodiments,” etc., may indicate that the embodiment(s) of the invention so described may include a particular feature, structure, or characteristic, but not every embodiment necessarily includes the particular feature, structure, or characteristic. Further, repeated use of the phrase “in one embodiment,” or “in an exemplary embodiment,” do not necessarily refer to the same embodiment, although they may.

In the following description and claims, the terms “coupled” and “connected,” along with their derivatives, may be used. It should be understood that these terms may be not intended as synonyms for each other. Rather, in particular embodiments, “connected” may be used to indicate that two or more elements are in direct physical or electrical contact with each other. “Coupled” may mean that two or more elements are in direct physical or electrical contact. However, “coupled” may also mean that two or more elements are not in direct contact with each other, but yet still co-operate or interact with each other.

An algorithm may be here, and generally, considered to be a self-consistent sequence of acts or operations leading to a desired result. These include physical manipulations of physical quantities. Usually, though not necessarily, these quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It has proven convenient at times, principally for reasons of common usage, to refer to these signals as bits, values, elements, symbols, characters, terms, numbers or the like. It should be understood, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities.

Unless specifically stated otherwise, as apparent from the following discussions, it may be appreciated that throughout the specification discussions utilizing terms such as “processing,” “computing,” “calculating,” “determining,” or the like, refer to the action and/or processes of a computer or computing system, or similar electronic computing device, that manipulate and/or transform data represented as physical, such as electronic, quantities within the computing system's registers and/or memories into other data similarly represented as physical quantities within the computing system's memories, registers or other such information storage, transmission or display devices.

In a similar manner, the term “processor” may refer to any device or portion of a device that processes electronic data from registers and/or memory to transform that electronic data into other electronic data that may be stored in registers and/or memory. A “computing platform” may comprise one or more processors.

Embodiments of the present invention may include apparatuses for performing the operations herein. An apparatus may be specially constructed for the desired purposes, or it may comprise a general purpose device selectively activated or reconfigured by a program stored in the device.

In yet another exemplary embodiment, the invention may be implemented using a combination of any of, e.g., but not limited to, hardware, firmware and software, etc.

While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should instead be defined only in accordance with the following claims and their equivalents. 

1. A weapon flyout simulation method, comprising: modeling a target as a plurality of ellipsoidal zones corresponding to a plurality of zones on the target; and determining whether a trajectory of a weapon interferes with at least one of said plurality of ellipsoids.
 2. The weapon flyout simulation method of claim 1, further comprising: determining whether a the weapon has reached a closest point of approach of the target.
 3. The weapon flyout simulation method of claim 2, wherein said step of determining whether a the weapon has reached a closest point of approach of the target comprises: determining a relative position of the target with respect to the weapon; calculating an engagement closure state for the weapon based on said relative position; comparing said engagement closure state to a previous engagement closure state; and denoting that said closest point of approach has been reached based on a change in said engagement closure state.
 4. The weapon flyout simulation method of claim 2, wherein said step of determining if said trajectory of the weapon interferes with at least one of said plurality of ellipsoidal zones comprises: computing an elliptical magnitude at said point of closest approach based on parameters relating to said at least one ellipsoidal zone; and determining whether said trajectory of the weapon interferes with said at least one ellipsoidal zone based on said elliptical magnitude.
 5. The weapon flyout simulation method of claim 1, further comprising: transforming a trajectory of the weapon to a target zone coordinate frame for each of said plurality of ellipsoidal zones; wherein said step of determining whether a trajectory of a weapon interferes with at least one of said plurality of ellipsoids is performed using said trajectory of the weapon in said target zone coordinate frame.
 6. The weapon flyout simulation method of claim 5, wherein said step of transforming a trajectory of the weapon comprises: determining coordinates of the weapon and the target in an engagement coordinate frame; transforming a trajectory of the weapon from said engagement coordinate to a target body coordinate frame; and transforming said trajectory of the weapon from said target body coordinate to said target zone coordinate frame for each of said plurality of ellipsoids.
 7. The weapon flyout simulation method of claim 1, further comprising: computing impact coordinates on the target.
 8. The weapon flyout simulation method of claim 7, wherein said step of computing impact coordinates comprises: calculating impact coordinates in a target zone coordinate system based on a point of closest approach for at least one of said plurality of ellipsoidal zones; and determining impact location in a target body coordinate system by rotating said impact coordinates from said target zone coordinate system.
 9. The weapon flyout simulation method of claim 1, further comprising: computing a miss distance of the target by the weapon.
 10. The weapon flyout simulation method of claim 9, wherein said step of computing a miss distance of the target by the weapon comprises: computing a first vector representing said trajectory of the weapon; computing a second vector representing a distance a first trajectory point of the weapon and a centroid of at least one of said plurality of ellipsoidal zones; computing a third vector indicating a direction of a line running from said centroid of said at least one ellipsoidal zone perpendicular to said first vector based on said first and second vectors; scaling a magnitude of said third vector to unity to obtain a unit direction vector; and computing a miss vector based on a dot product of said unit direction vector and said second vector.
 11. The weapon flyout simulation method of claim 1, further comprising: assessing impact damage on said target.
 12. The weapon flyout simulation method of claim 11, wherein said step of assessing impact damage is based on at least one of a weapon lethality, a target survivability, or a zone sensitivity of at least one of said plurality of ellipsoidal zones.
 13. The weapon flyout simulation method of claim 11, wherein said step of assessing impact damage comprises: determining a weapon lethality of the weapon; determining an effective lethality of the weapon on the target based on said weapon lethality and a zone sensitivity of at least one of said plurality of ellipsoidal zones; and determining if said effective lethality exceeds a survivability threshold of the target.
 14. The weapon flyout simulation method of claim 1, further comprising: assessing damage to the target based on proximate detonation of the weapon.
 15. The weapon flyout simulation method of claim 14, wherein said step of assessing damage to the target comprises: computing a miss distance to a centroid of at least one of said plurality of ellipsoidal zones; computing a range loss for said miss distance; determining weapon lethality of the weapon; determining effective lethality of the weapon on the target based on said weapon lethality, a zone sensitivity of at least one of said plurality of ellipsoidal zones, and said range loss; and determining if said effective lethality exceeds a survivability threshold of the target.
 16. The weapon flyout simulation method of claim 1, wherein said target comprises an aircraft.
 17. The weapon flyout simulation method of claim 16, wherein said plurality of zones on the target comprise at least one of: a circumscribing sphere; a forward fuselage; an aft fuselage; a left sing; a right wing; a left rear stabilizer; a right rear stabilizer; a vertical stabilizer; and an extra surface.
 18. A weapon flyout simulation system comprising: a target modeling unit adapted to model a target as a plurality of ellipsoidal zones corresponding to a plurality of zones on the target; and a hit/miss assessment unit adapted to determine if a trajectory of a weapon interferes with at least one of said plurality of ellipsoids.
 19. The weapon flyout simulation system of claim 18, further comprising: a closest point of approach determination unit adapted to determine if the weapon has reached a closest point of approach of the target.
 20. The weapon flyout simulation system of claim 19, wherein said hit/miss assessment unit is adapted to compute an elliptical magnitude at said point of closest approach based on parameters relating to said at least one ellipsoidal zone, and determine whether said trajectory of the weapon interferes with said at least one ellipsoidal zone based on said elliptical magnitude.
 21. The weapon flyout simulation system of claim 18, further comprising: a coordinate transformation unit adapted to transform a trajectory of the weapon to a target zone coordinate frame for each of said plurality of ellipsoidal zones; wherein said hit/miss assessment unit determines if a trajectory of the weapon in said target zone coordinate frame interferes with at least one of said plurality of ellipsoids.
 22. The weapon flyout simulation system of claim 18, further comprising: an impact coordinate computation unit adapted to compute impact coordinates on the target based on a point of closest approach for at least one of said plurality of ellipsoidal zones.
 23. The weapon flyout simulation system of claim 18, further comprising: a miss distance computation unit adapted to compute a distance by which the weapon has missed the target.
 24. The weapon flyout simulation system of claim 18, further comprising: an impact damage assessment unit adapted to assess impact damage on said target based on at least one of weapon lethality, target survivability, or zone sensitivity of at least one of said plurality of ellipsoidal zones.
 25. The weapon flyout simulation system of claim 18, further comprising: a proximate damage assessment unit adapted to assess damage to the target based on proximate detonation of the weapon.
 26. The weapon flyout simulation system of claim 18, wherein said target comprises an aircraft and said plurality of zones on the target comprise at least one of: a circumscribing sphere; a forward fuselage; an aft fuselage; a left sing; a right wing; a left rear stabilizer; a right rear stabilizer; a vertical stabilizer; and an extra surface.
 27. A computer readable medium embodying program logic, which, when executed, performs a method comprising: modeling a target as a plurality of ellipsoidal zones corresponding to a plurality of zones on the target; and determining whether a trajectory of a weapon interferes with at least one of said plurality of ellipsoids. 